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4 years ago

Multiply and simplify: cos(theta) sin(theta) (csc(theta) + sec(theta))

1 answer:

6 0

Cos(θ)sin(θ)[csc(θ) + sec(θ)]
cos(θ)sin(θ)[csc(θ)] + cos(θ)sin(θ)[sec(θ)]
cos(θ)sin(θ)csc(θ) + cos(θ)sin(θ)sec(θ)
cos(θ) + sin(θ)

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Is the number rational or irrational?

lapo4ka [179]

1. irrational: √48 = 6.92820323028

2. rational: √9 = 3

3. irrational: √39 = 6.2449979984

4. rational: √289 = 14

6 0

3 years ago

In june 2005, Peter mailed a package from his local post office in Fayetteville North Carolina to a friend in Radford, virginia

den301095 [7]

The total price that Peter paid for the local parcel = $2.07

The rate per ounce at that time was = $0.23/ounce

Total weight of Peter's package = Total price paid by peter/ rate per ounce

Total weight of Peter's package = $2.07/$0.23 per ounce

We now have to divide 2.07/0.23 = 207/23 (Shifting both numerator and denominator by 2 decimal places) = 9

Total weight of Peter's package = 9 ounces

8 0

3 years ago

The number s is one third the number t. Which number sentence shows the relationship between s and t?

Mashcka [7]

S= 1/3t (T is one third of s)

8 0

3 years ago

The city of Omaha decided to build a new parking garage in hopes of luring more people to the Old Market district.The city will

dimulka [17.4K]

Answer:

Given:

Mean, u = 135

Sample size, n = 42

Sample mean, x' = 126

Standard deviation = 16

Significance level = 0.05

1) The null and alternative hypotheses:

H0 : u = 135 (the revenue per day is $135)

H1 : u < 135 (the revenue per day is less than $135)

2) In this case, we have a left tailed test.

Let's use the formula:

$= \frac{x' - u}{s/ \sqrt{n}} = \frac{126 - 135}{16 / \sqrt{42}} = -3.645$

t = - 3.645

Critical value: at a significance level of 0.05, left tailed test,

tcritical = -1.683

We reject null hypothesis, H0, since t calculated, -3.645 is less than tcritical, -1.683.

3) Given, a = 0.05, df = 41, left tailed test,

t-value = 2.02

For the corresponding confidence interval, we have:

$CI = (x' - \frac{t * \sigma}{\sqrt{n}}, x' + \frac{t * \sigma}{\sqrt{n}})$

$CI = (126 - \frac{2.02 * 16}{\sqrt{42}}, 126 + \frac{2.02 * 16}{\sqrt{42}})$

CI = (121.014, 130.986)

4) Conclusion:

We reject the estimated potential revenue advised by the consultant, H0, as it is too high, because the t-calculated falls in rejection region(i.e, less than critical value), also the upper limit of the confidence interval is less than $135.

5 0

3 years ago

Which components are a possible representation of vector w if the magnitude of vector -3w is ||-3w||=15?

Black_prince [1.1K]

Answer:

<-3,4>

<0,-5>

Step-by-step explanation:

|-3w| = 15

3|-w| = 3|w| = 15

|w| = $\frac{15}{3}$

|w| = 5

If vector w is represented by <1,-9>

Then |w| = $\sqrt{(1)^{2}+(-9)^{2}}=\sqrt{1+81}=\sqrt{82}\neq5$ .

Therefore this is not possible.

If vector w is represented by <-3,4>

Then |w| = $\sqrt{(-3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}=5$ .

Therefore this is possible.

If vector w is represented by <4,5>

Then |w| = $\sqrt{(4)^{2}+(5)^{2}}=\sqrt{16+25}=\sqrt{41}\neq5$ .

Therefore this is not possible.

If vector w is represented by <-5,-3>

Then |w| = $\sqrt{(-5)^{2}+(-3)^{2}}=\sqrt{25+9}=\sqrt{34}\neq5$ .

Therefore this is not possible.

If vector w is represented by <0,-5>

Then |w| = $\sqrt{(0)^{2}+(-5)^{2}}=\sqrt{0+25}=\sqrt{25}=5$ .

Therefore this is possible.

(NOTE : if z vector is represented by <x,y> then |z| = $\mathbf{\sqrt{x^{2}+y^{2}}}$ )

4 0

3 years ago